Hob for cutting involute gears.



g O. G. SWEMUNS. HOB Hw @mum xNvoLmE GEMS.

UNITED STATES,- PATENfi* orifice. y

i GLIVER G. SIMMGNS, '0F ROCHESTER, NEVI' YORK.

HOB FOB CUTTING INVGLUTE GEARS.

Tocll'wlwm t may concern: Y l

Be it known that 1, OLlveii G. SIMMoNs, a citizen of the United States, residing in Rochester, in the county of Monroe and State, of New York, have invented new and has for itisv general ohJect to produce 'a hobi hing' cutter which will adinit'of the gears clit thereby being interchangeable with other gears ofthe same diainetral pitch and systein, whether such other gears have been cut in'a niillinginachiiie, hohhingr machine, or in a gear planer, thereby avoiding any necessityfoi" an empirical modification of the tooth curve. t I

Stated iridetail objects ol: the invention areto produce ii hob having a novel con- A struction of teeth arranged in the forinhof a helix,"which will, in operation, result in the generation of true involute c'urves on the teeth of spur gears, said curves extending from `the imaginary base circle to the perinheif" of the gear, to produce a helical hob having a lead, measured on the angle of the helix, which will equal, the hase circle pitch of the gear. being cut; to provide the teeth of the liobliiiig cutter with a circular cutting piint in the forni' of a curve of n cirele,

preferably a eeiiiivcirele, for producing a curved clearance space at the Yroots of ad- ;jacent teeth; and to provide a lieb/the cutting points ofthe teeth whereof are conge'r 'when the lineal movement of saidrack tooth is directly' proportioned tothe moveiiient `of the involute curve, In practice,

specinmion of Leners raient.

tooth,l presents" only one pointe- 'contact 4for the ,teeth of the mating j owing to the wearing oi such teeth, their use would not be 'feasiblel lt is important to know this, however, for the reason that it isV the general practice to make the form adopted for the rack tooth the kcy'to any system of gearing: and this for the reason that i'l" all gears ot' the system. will mesh with the rack it necessarily follows that they will mesh with one another. vit will he shown, however, that the inclination ol' the `sides ol' the rack tooth is scientifically incorrect when it is desired to hai e the lineal movement oi' such rack tooth directly proportioned to the movement ol the inrolnte curve in Contact, and that therefore there canbe no true roiling movement divertir profnirtioncd to the involutr` curves of the hase circle between 'a spur gear. haring involnte (voili and snc-h :i rack. .lt therefore holds that il a rack having the sides of the teeth inclined ".v-ill not produce a true rolling movi-:ovni directly proportioned to the lead of the mating involute curves when in mesh with an nivo luie gear, a liolibing cutter, the sides of whose teeth are inclined, n ill not cat gears haring teeth with true inrolnte cai-ws of the base circle if the lineal movement of the counter parl rack is directly proportioned to the lead of said invol'ute curves.

The present invention. therefore. is hased on the principle that the teeth oi' the hob, witha normal lead equal to the hase circle pitch, to eut gear teeth having tr ue involutecurved sides, must have parallel sides er cntn ting edges; or, moreV accurately stated, the

cutting points of the teeth ninst lie in par-y allel lines erpendicular` to the axis-of the hob. -l will now proceed to describe my invention ,and to demonstrate the accuracy of the principle involved, having reference to the accompanying drawings, in whiclr- Figure 1 is a Sectional view showing my Vimprovedhob in connection with a lQ-tooth gear of 2diametra1 pitch. and show ing the cutting of the geur as having been completed by the hob. In this view, the teeth of the hob are sectioned -on the lines 3;-3. 4.--4, 5 5, et'cl, of Fig. 3 and have all of their faces bron ht "to the same longitudinal plane?, for t ie urpose of enabling the meas urenients of vtie teeth to lie-clearly shown, with reference to the gear being cut; and

Pai exited Sept. 25, 191 7.

Appiibaaon mea November e, isis. smal No. 129,670.

the body of the hob below the teeth is shown as a true longitudinal section.

Fig. 2 is a view in end elevation of 'a hob;

Fig. 3 is a plan view of the same; and

Fig. el is a diagrammatic view illustrating the extent to which a rack havin teeth with inclined sides will be advanced eyond the true mating distance by contact with a tooth having `a true involute curve.

Referring now to Fig. l, the numeral 1 indicates the bobbing cutter as it ,would appear when generating the teeth 2 of the gear, indicated bythe numeral 3. The section shown of the hobbing cutter 1 is taken on a line perpendicular to the angle of the helix of the right-hand threaded hob, as indicated by the section lines in Figs. 2 and 3 on which Fig. l is taken. The numeral 4 indicates the lead or pitch of the hob 1, measured on the angle of the helix, said lead being equal to the base circle pitch of the gear 3. The base circle pitch is the distance between the teeth 2 of the gear 3 measured on the base circle.

The numeral 9 indicates the teeth of` the hob, and for reasons which will hereinafter be demonstrated, these teeth have their cutting points confined within parallel lines which are perpendicular to the axis of the hob and, as above shown, have a normal pitch vequal to the base circle pitch of the gear being cut. As will later be shown, the teeth 9 do not have to .be straight-sided, for the reason that in operation a single point only enerates the involute curve, but the straig t sides are a convenient form of construction. In the gear 3 the adjacent involute curves of the lteeth are joined by a curved line from the points of origin of the curves on the base circle 14', said curve having a radius indicated by the numeral 8. In order to generate this curve the teeth 9 of the hob 1 are provided with curved outer ends, each of id curves having a radius 10 equal to ie radius 8. These curves join the straight sides of the teeth 9 at the point of intersection of the base line 14 therewith, said base line 14 corresponding in the hob with the root circle 14 of the gear. As will more clearly hereinafter appear, the eective parts of the teeth 9, so far as generating true involute curves in the cutting of the teeth of the gear is concerned, are the points of intersection of the curved lines of the teeth with the base line 14. Below these points theteeth of the hob may therefore have any desired form of clearance. In order to demonstrate the correctness of the position that only a single cuttin point on either side of each tooth of the'ho generates the involute curve1 of the teeth cut, I submit the follbwing demonstration, based upon the illustrationof Fig. 4; first premising that an involute curve has an unvarying and deiinite lead when measured on a line tangent to the evolute, or the gen `erating circle. This truth may be stated in the form of a law, as follows:

The involute of any evolute has a constant lead when measured on a line tangent to said evolute, and is equal to the perimeter of the generating evolute.

Referring now to said Fig. 4, the numeral 26 indicates involute curves generated according to the above law and having as an evoluto the circular disk indicated by the numeral 25. The involute curves 26 have been generated equidistant over one-half of the periphery of the disk 25. The numeral 27 indicates a line tangent to the disk 25 at the point 28. Passing through the point 28 and the center of the disk 25 is the line 29. The line 29, therefore, is erpendicular to the line 27. The line 27' is tangent to the disk 25 and parallel to the line 27. The point of tangency 28 of the line 27 is the point of origin of the involute curve 26', 'iso that the numeral 30 indicates the lead of the involute curves 26' and 26, because all invclutes generated from the same evolute are equal, and the measure is taken on a line parallel to the tangent line 27, the involute curve 26 being shown as extending through one complete revolution or spire.

Since all involute curves 'enerated from the same circle, but from di erent points of origin, are parallel, and since the involute curves 26 and 26' are equi-distant on the periphery of the circle of the disk 25, it follows that the measures 31, 31 and 31 between the parallel lines 32 are equal. The lines 32 are parallel and tangentto the i11- volutes 26 and 26'; they must, therefore, be perpendicular to some tangent line to the circle of the disk 25, because all tangentsto an involute are also perpendicular to the tangent to the evolute; and the point of tangency of the tangent to the involute is also the point of intersection of the two tangente. From this it is seen that the tangent lines 32 are perpendicular to the tangent line 27. In like manner it can be shown that the lines 8B are tangent to the nvolute curves 26 and 26', and erpendicular to the tangent line 27', and tlat the are equi-distant. v It follows, further, tha the sum of the measure between the lines 32 or 33, as represented by the numerals 31, 31 and 31, will be equal to one-half of the lead of the involute curve 26', as measured on the tangent line 27, such measure being indicated by the numeral 34. The measure indicated by the numeral 34' will then represent the other half of such lead, and the sum of these measures will equal the lead 30 of the involute curve 26'. It is understood, of course, that the path of travel of a rack will necessaril be parallel to the tangent lines 27 and 2 and, as I allirm, the ilanks of Cil the teeth of the rack should be perpendicular to the tangent lines 27 and 27 1n order to have uniform linear motion according t0 the lead of the involute curves of the teeth of the mating gear.

To prove the above truth let the line a-b, Fig. el, drawn at an angle of 45 to the tangent line 27', represent one side of Va rack tooth, and the involute curve 26 represent one side of a tooth of a gear in engagement with said rack tooth; it will now Vbe shown that the lineal movement of this tooth a--b will exceed the lead of the mating involute 2G, which is the true movement, by .over forty-one per cent. The line b-c is drawn tangcntto the disk circle 25 and at an an le of 450 with respect to the tangent .line 2 The line a-b is also tangent to the involute curve 26, as shown; the lines a-b and b-'c" will therefore form a right angle, or an anlgle of 90; and if from the point of intersection c of the line b-c with the involute curve 26 the line c-a be drawn arallel to the tangent line 27", the triange a-?1-c will he formed having the sides c-b and b-Y equal. This trianglewill then re nesent the tooth of the rack, and if the dis 25 is turned in the direction ot' the arrow the involnte curve 26, beginning at the point of tangency Ab, will slidingly engage over the whole of the length of the line b-a, moving the triangle aub-*0 along the base a-c parallel to the tangent line 27 until the en a. of the line c-b coincides with c, when the involute curve 26 will have assumed the position of the involute curve 26' and the circular disk 25 will have natie one-half a between the i The engagement curve 26 and the line 47,-?) is shown successively by the short lines o perpendicular to b--rf and tangent to the involute curves 26 and 26'. As the end a of the line a-b will coincide with the end c of the line )c at th termination of the above movement., the triangle afb-o will have moved `to the right. through a distance equal to the line (L -Ic, which distance vis indicated by the numeral 35. It is seen by inspection that the distance indicated by the numeral 35 is greater .than that indicated by the numeral 34, which, as has been previously stated, is the true dist-ance. It will now'be seen that revolution.

when the flank of a rack tooth is inclined at an angle to the perpendicular to the tangent liuc (the line of travel of the rack) there will result this radual forging ahead of the rack, as above t iagraInmat-ically illustrated; and this fart together with the use oi" a long addendum and dedendum and small pres siiire angle, has made it necessary therefore to modify and correct the teeth of the rat-lc at the outer portion of the faces amLlianlts "in order to permit a gear to mush at all with the rack. This distance traveled by the tooth of the rack in excess of the true dis Ahalf the lead, or 2.375` inches.

,The leads of the mamas e6 and ce win; therefore, according to4 the above, be equal to 4.75 inches. 1f, now, the involute curve .26 is in contact with a rack tooth the ilanlis of which are perpendicular to the tangent line 27, and the disk is given one-half a revolution, half of the lead, or 2.375 i11chcs. It, however, the rack tooth is inclined at an angle of 450 to the tangent line 27 the contact will be along the line a-J, which, by inspection, we see equals 2.375 inches, because a-b equals b-c and b-c is 25, and since the line b--o is doter-min d by the distance between the involute curves 2G and 2G', which represent one-half the load, tlieline a-Z1, therefore, must equal one- ()ne side of the triangle a-b-c has been determined, and we know that the angle L -b-c equals 90; it follows that the distance represented by the numeral 35, ortheI measure of the line a0, must be equal to the square root of the sum of the squares of LM- and b-c which, upon solving, we find equal to 3,3586 inches. Subtractiiugr 2.375 from 3.3586 leaves .9836 inch, which is the distance traverSed by the ruck tooth in 'excess of the true distance, and which it is seen is over fort -one per cont. greater than the rack toot should have traveled. In an)r rack with inclined teeth described, meshing with a true involute curve, itcan. be shown that the forging ahead amounts to the difference in the lead of the involute curves ofi the base circle and pitch circle selected.

Applying this same demonstration to a hob, the relation of the teeth of which to a gear is, in principle, identical with that of the relation between the teeth of a rack with a geurl` it is made evident that the teeth of the hoh should have teeth flanks which will not come in contact with' the involutc curved surfaces of the teeth; shou'lil be inclined perpendicular to the pressure angle lilies. as 'is nowthe custom, and give-n .i lineal movement directly proportioned to the lend of the involute curve of the base circle selected. the resultant und thatif these sides the rack tooth will move onetangent to thc disk curve of the teeth eut thereby could not possibly be in the form of true involute curves to the selected base circle, but would be curves vto some other circle smaller in diameter than the circle selected. As a matter of fact, while it is true that involute gears as now manufactured represent a very great advance over the old epicycloidal system of gearing, it is equally true that neither hobbed,

laned nor milled gears, will run quetl and 1t is further true that such gears will not mesh accurately with one another if the mating pair of gears were not cut by the same method. This is due to the fact that such gears are not made in accordance with the law which I have demonstrated in my application hereinafter referred to to be a universal law governing the generation of all involute curves, and to other causes which have been referred to. It only becomes necessary to observe the scientific principle governing the generation of the curve in its application to all forms of machines or cutters used in manufacturing involute gears to obtain gears which will be absolutely interchangeable irrespective of the fact whether such gears have been cut or generated according to one or the other of the methods of manufacture now employed because the principle is the same in all cases. Hence, gears of a given diametral pitch cut by any one of these methods will necessarily mate with a gear of the same diametral pitch cut by any other method so long as in cutting the teeth the involnte curve is produced in accordance with the law which I have heretofore demonstrated to be scientically correct. Such gears will run quietly, willbe characterized by freedom from wear, when the mating gears have an equal number of teeth, and a minimum of wear in all other cases; the involute curve of the teeth will extend from the root circle to the periphery ofthe tooth, the teeth will be stronger, -andtliere will be an utter absence of interferencebetween the teeth. It is furthermore possible to produce a standard of gearing o f known form, which can be laid out by any mechanic or engineer who desires to employ it, and to avoid any necessity for an empirical modication of the tooth curve.

In my yapplication for patent for an in.

volute gear, Ser. No. 97,530, filed Ma 15th, 1916, I have given the dimensions an measurements of a twelve-tooth gear Wheel of 2 diametral pitch corresponding to the gear 3 of the present application' It seems unnecessary, therefore, to go into detail inV describing this gear, as the measure of the base circle pitch, which hasbeen given above is the essential factor in determining the lead of the teeth of the hob. For convenience of reference, therefore, I will simply state that the pitch circle radius 5 is equal to 3 inches.

The addendum is equal to of the module or diametral pitch; the radius 6 of the periphery or outside circle of the gear 3 will be equal to Sfg inches; the radius 7 of the base circle is equal to 2.7716; the pressure angle is 225C; the diameter of the base circle will e ual 5.5432 inches; and the perimeter of said base circle will equal 174045+ inches. The base circle pitch, which is found by dividing the perimeter of the base circle by the number of teeth (12) in the gear, equals 1.45037 inches. It is to be notedV that the measure given above for the base circle pitch Willl always equal that for any number of teeth so long as the diametral pitch is 2. In a similar Way the circular pitch, measured on the pitch circle. is obtaix1ed,fand is found to equal 1.5708 inches.

Since it is a practice in gearing to have the teeth in gears of the same diametral pitch of equal thickness on the pitch circle, to permit interchangeability, and so that the teeth will have equal strength, said tooth thickness being made equal to el* of the circu lar pitch, for lthe same reasons I have made the teeth of like thickness in the gear 3, shown in the drawings. The thickness of the teeth measured on the root or base circle will, of course, be greater than when measured on the pitch circle, as is obvious from a mere inspection of the drawing.v

It now remains to determine the measure of the radius 8 of the curve joining the involute curves of the teeth so that the incasure of the radius 10 of the curves of the teeth of the hob may be determined.

In Fig. 1 on the gear 3, which is the base gear, there is the right triangle e--a--f with the line d-f coinciding with the pressure angle line g-g, and since the pressure angle equals 22.1` degrees in the gear shown, the angle d-e-f will equal 222; degrees because the line dc is a radial line and perpendicular to the line g-g at the oint of tangency of said lineg-g with the ase circle 14. Then the line f-al must equal the line e-f multiplied by the sine of the angle d-e-f, Which measure I find is equal to 1.14804 inches. But the line d-*f is a tangent line to the base circle intersecting the lnvolute curve of thc tooth at the itch circle 15; therefore, the line df will e equal to the curved line d-i of the base circle 14", which is in accordance with the law of the involutc as heretofore referred to. curved line d--L then will have"a measure equa] to 1.14804 inches.

Subtracting the measure of the line a--h from the base circle pitch (1.45037) leaves as a result .3023 inch as the measure of the arc on the base circle 14', which is indicated by the radius numeral 8; and this for the reason tha-t the difference between a straight line and the curved one referred to is so small as to be Wholly negligible in this The connection so that. the measure of the arc ma be used as that of the radius 8.

s the curves of the teeth of the hob must necessarily 'have the same measure as the radius 8 it follows that a bobbing cutter for a 2 diametral pitch geur of twelve teeth will haven peripheral tooth radius 10 equal to .3023 inch.

Since a radius represents the distance between 'a point on a circle and its center, and since it is known that all involute curves gencrrted from the base circle but from dill'erent points of origin, are parallel, for

`the reason that the lead remains the same,

it follows, and as shown in Fig. 1, and indicated by the numeral 11, that the semi circular arran ement of the periphery of the teeth 9 of ne hobbing cutter 1, will not only generate true involute curves, but also generate the curved -root clearance between the teeth, as shown. It is understood that the curve of the teeth 9 of the hob will always be tangent to the involute curve beinggenerated, in accordance with the principle demonstrated in Fig. 4. It will be under-K stood, of course, that the curved periphery of the teeth of the heb extending as they do below the base circle of the gear and.beyond the base line 14 of the hob, could not themselves nente involute curves originating on theease circle 14. In referring, therefore, to the generation of involute curves .by these curved cutting` surfaces it will he understood that I refer to the cutting away of material beyond the involute curve by said curved surfaces and to a point corre-- spending to the intersection of said curves with thestraight sides of the'teeth or with the base line 14, which points, on either side of the teeth, are theoretically the cutting points which must generate the involute curve in accordance with the law governing the' p neration of the involutc curves above refe red to. p

It is understood that, as usual in the operation of h obs, my improved hohhing cutter will be set at an angle to the gear to he cut, according to the angle of theI helix of theV hob, as indicated by the numeral lil/j'v (Fig. 3). The measure indicatedby the numeral 4 is usually termed the normal pitchl and, as shown, is on the angle of the helix. The actual pitch, or the pitch for which lthe lathe will be geared to cut the teeth El,

is indicated by the numerall 13. The depth of the teeth 9 of the hohhing cutter l indi cated b the measures a, b, andthe radins c, from t c base line 14, Fig. ,1, may heV anything that vwill give suflicient clearance he y 00 tween the hoh and' the teeth 2 of the .freer 3.

The thickness of the teeth 9 of the hob will, as previously stated, equal twice the radius 10 of the curved periphery of the teeth.

My improved hobhing cutter is fluted at right angles to the angle of the helix of the hoh, :is shown in lligs. Q and 3. The angle of the helix may easily he obtained, hut since it forms no part of' the present invention it will be suiiicient to state that this angle is determined by the use of the right :ingle triangle n, Fig. 3.

I claim:

1. A hoh for cutting: involuteI fears of a given dizunetrical pitch having a normal lead substantially equal to the hase' circle pitch of the geur adapted to he eut.

2. A hoh for cutting im'ohdc gears provided with straight-sided teeth pelpendicu lar to thc axis of the hoh.

3. A hob for cutting involute gears having the cutting points of its teeth confined within parallel lines defining the width of the teeth at the base line of the hob.

4. A. hob for cutting iuvolute ,gears having the cutting peints of its teeth conned within parallel lines defining the width of the teeth at the base line of vthe hob and lyingwholly on said base line.

5. A heb having teeth either side of said teeth having a single invalide-generating point.

6. A hob for cutting involute gears the cutting teeth whereof are provided with curved peripheral cutting points.

7. A heb for cuttin involute gears, the cutting teeth whereo are provided with peripheral cutting points having the form of e curve of a circle with a radins corresponding: to one-halt of the arc between the adjacent iuvoluie curves of the gear measured on the hase circle of the base gear.

8. A hoh for cutting involute gears the teeth whereof from the hase line of the hob to the base of thc teeth are of any desired depth, the cutting points of said teeth being confined within parallel lines and each tooth having n curved peripheral cutting end, the curve'of which connects the sides of the teeth of the hoh at the point of intersection therewith of the hase line.

' 9. A hoh for cutting' involulc gears 'having u normal pitch equal to ihr hase circle pitch o'l' the ,your to he cui'. and the teeth wlwreof have their cutting points confined f within parallel lines per|n-ndiculur to the axis of the hoh.

ln testimony whereof' l have hereunto set my hand.

LIVFJR l. SIMMONS. 

